B Solenoid B field lines question

Hi, I wonder what would the path of magnetic field be in my case.I have a solenoid , it's a metal rod that has a winding in the middle of it, I need the magnetic field to come out of the rod not at the ends of it as is usually shown in pictures but at the surface side along each end of the metal rod.If I place the solenoid in a metal pipe with a slightly larger diameter would most of the field lines then exit the solenoid after the winding end at each side and enter the outer metal encasing to flow back to the other side?
I need the field between the rod and the outer pipe to be perpendicular to the surface so my question is will this arrangement do this?
I have attached a crude drawing of the supposed idea.

One reason you aren't getting replies is that the behavior of magnetic field lines in the presence of iron is highly non-linear, and often the results are non-intuitive. (One example is that iron cores can saturate in some regions where the B field is intense. This alters the behavior everywhere, both elsewhere in the core as well as outside, and potentially even in your outer flux return structure.) This problem is a good candidate for analysis using one of the standard numerical simulation packages (Ansys or COMSOL, e.g.)